# Finding intervals where the second derivative is positive

## 1 Answer

$$f'(x)=15x^4−30x^2.$$

\[f''(x)=60x^3-60x=60x(x^2-1)=60x(x+1)(x-1).\]

The roots of $f''(x)=60x(x+1)(x-1)$ are $x=0, x=1, x=-1$. Hence $f''>0$ on the following intervals

\[(1,\infty) \text{and} (-1,0).\]

We can also see that Hence $f''<0$ on the following intervals

\[(-\infty,-1) \text{and} (0,1).\]

Savionf

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